scholarly journals Analysis of regularized least-squares in reproducing kernel Kreĭn spaces

2021 ◽  
Author(s):  
Fanghui Liu ◽  
Lei Shi ◽  
Xiaolin Huang ◽  
Jie Yang ◽  
Johan A. K. Suykens
Keyword(s):  
Least Squares ◽  
Reproducing Kernel ◽  
Regularized Least Squares ◽  
Krein Spaces

Learning rates for regularized least squares ranking algorithm

2017 ◽  
Vol 15 (06) ◽  
pp. 815-836 ◽  
Author(s):  
Yulong Zhao ◽  
Jun Fan ◽  
Lei Shi
Keyword(s):  
Least Squares ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Ranking Algorithm ◽  
Generalization Error ◽  
Ranking Problem ◽  
Regularized Least Squares ◽  
U Statistics ◽  
Learning Rates ◽  
Error Decomposition

The ranking problem aims at learning real-valued functions to order instances, which has attracted great interest in statistical learning theory. In this paper, we consider the regularized least squares ranking algorithm within the framework of reproducing kernel Hilbert space. In particular, we focus on analysis of the generalization error for this ranking algorithm, and improve the existing learning rates by virtue of an error decomposition technique from regression and Hoeffding’s decomposition for U-statistics.

RPC Estimation via $\ell_1$-Norm-Regularized Least Squares (L1LS)

2015 ◽  
Vol 53 (8) ◽  
pp. 4554-4567 ◽  
Author(s):  
Tengfei Long ◽  
Weili Jiao ◽  
Guojin He
Keyword(s):  
Least Squares ◽  
Regularized Least Squares
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